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3.Factorise:
(i) \(x2 + xy + 8x + 8y\)

(ii) \(15xy – 6x + 5y – 2\)

(iii) \(ax + bx – ay – by\)

(iv) \(15pq + 15 + 9q + 25p\)

(v) \(z – 7 + 7xy – xyz\)


Answer :

(i)We have: \(x2 + xy + 8x + 8y\)

now, grouping the terms, we have \(x2 + xy + 8x + 8y\)

\(= x(x + y) + 8(x + y)\)

\(= (x + y)(x + 8)\)

Thus, the required factors =\((x + y)(x + 8)\)

(ii)We have: \(15xy – 6x + 5y – 2\)

Now, grouping the terms, we have \((15xy – 6x) + (5y – 2)\)

\(= 3x(5y – 2) + (5y – 2)\)

\(= (5y – 2)(3x + 1)\)

Thus, the required factors =\( (5y – 2)(3x + 1)\)

(iii) We have: \(ax + bx – ay – by\)

Now, grouping the terms, we have \(= (ax – ay) + (bx – by)\)

\(= a(x – y) + b(x – y)\)

\(= (x – y)(a + b)\)

Thus, the required factors = \((x – y)(a + b)\)

(iv) We have: \(15pq + 15 + 9q + 25p\)

Now, grouping the terms, we have \(= (15pq + 25p) + (9q + 15)\)

\(= 5p(3q + 5) + 3(3q + 5)\)

\(= (3q + 5) (5p + 3)\)

Thus, the required factors = \((3q + 5) (5p + 3)\)

(v) We have:\(z – 7 + 7xy – xyz\)

Now,grouping the terms, we have \(= (-xyz + 7xy) + (z – 7)\)

\(= -xy(z – 7) + 1 (z – 7)\)

\(= (-xy + 1) (z – 1)\)

Thus, the required factor =\( -(1 – xy) (z – 7)\)